## [1] "Run Completed at 2018-02-06 15:07:53"
\[ Yobs_{i,j} \sim Bernoulli(N(0,1.68)) \]
Note that this is a random probability of interaction on a per observation basis. This is different than a random link model. If we are interested in a binary network, a random interaction probability model will lead to a link probability of 1-(1/2)^n in n sampling events.
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 0
## Unobserved stochastic nodes: 1933
## Total graph size: 9379
##
## Initializing model
\[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 605
## Unobserved stochastic nodes: 1328
## Total graph size: 8821
##
## Initializing model
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect.jags")
## cat("
## model {
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation Process
## #True state
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## p[x]<-z[x] * s[x]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## pnew[x]<-znew[x]*snew[x]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 605
## Unobserved stochastic nodes: 2871
## Total graph size: 11906
##
## Initializing model
# Incorportating species occurrence
If species co-occurrence is a prerequisite for interaction, then the absence of interactions may stem either from a lack of detectability or species absence. We can jointly model the presence of species as a function of elevation and then existance of an interaction.
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect_Elevation.jags")
## cat("
## model {
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Occurrence Process
## logit(psi[x])<-alpha_occ[Bird[x]] + beta_occ[Bird[x]] * elevation[x] + beta2_occ[Bird[x]] * elevation[x]^2
## occ[x] ~ dbern(psi[x])
##
## #Is the species available to be detected?
## rho[x]<-detect[Bird[x]]*occ[x]
##
## #Observation Process
## #True state
## z[x] ~ dbern(rho[x])
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## p[x]<-z[x] * s[x]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## E[x]<-abs(Yobs[x]- s[x])
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## #Occurrence Process
## logit(psi_new[x])<-alpha_occ[NewBird[x]] + beta_occ[NewBird[x]] * elevation_new[x]
## occ_new[x] ~ dbern(psi_new[x])
##
## #Is the species present to be detected?
## rho_new[x]<-detect[NewBird[x]]*occ_new[x]
## znew[x] ~ dbern(rho_new[x])
##
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## pnew[x]<-znew[x]*snew[x]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Note: flat logit priorsm - Following lunn 2012 p85
##
##
## #Occurrence Priors
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta2_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
##
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior check
## fit<-sum(E[]) #Discrepancy for the observed data
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 605
## Unobserved stochastic nodes: 4440
## Total graph size: 19820
##
## Initializing model
## # A tibble: 4 x 4
## # Groups: Model [4]
## Model Presence Absence p
## <chr> <int> <int> <dbl>
## 1 Random 2473 327 88.3
## 2 Species 2174 626 77.6
## 3 Species_Detect 729 2071 26.0
## 4 Species_Detect_Elevation 748 2052 26.7
## [1] "True presence rate is: 11.1"
Dashed line is the observed network from the time-series.
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series. Note that this is really a measure of dissimilairty in one level (hummimngbirds), as the dissimilarity in plants is fixed by the sampling protocol. While there be a correlation between the species pool and the chosen plant to film, this is filtered by a human placing a camera at that plant, and as such isn’t a true measure of plant dissimiality.
Create a kind of venn diagram on PCA of model similarity based on per link discrepency.
## # A tibble: 19 x 3
## # Groups: Model [4]
## Model mean pair
## <chr> <dbl> <chr>
## 1 Species_Detect -1.00 Stripe-throated Hermit_Gasteranthus qu…
## 2 Species_Detect -1.00 Tawny-bellied Hermit_Columnea ciliata
## 3 Species_Detect_Elevation -1.00 Gorgeted Sunangel_Palicourea lineata
## 4 Species_Detect_Elevation -1.00 Stripe-throated Hermit_Gasteranthus qu…
## 5 Species_Detect_Elevation -1.00 Violet-tailed Sylph_Heliconia burleana
## 6 Species_Detect -0.967 Tawny-bellied Hermit_Centropogon solan…
## 7 Species_Detect -0.950 Tawny-bellied Hermit_Glossoloma oblong…
## 8 Species_Detect_Elevation -0.950 Buff-tailed Coronet_Meriania tomentosa
## 9 Species_Detect_Elevation -0.950 Collared Inca_Palicourea acetosoides
## 10 Species_Detect_Elevation -0.950 Tawny-bellied Hermit_Glossoloma oblong…
## 11 Random -0.850 Tawny-bellied Hermit_Columnea strigosa
## 12 Species -0.817 Tawny-bellied Hermit_Centropogon solan…
## 13 Random -0.800 Fawn-breasted Brilliant_Meriania tomen…
## 14 Random -0.800 White-whiskered Hermit_Heliconia burle…
## 15 Species -0.800 Stripe-throated Hermit_Gasteranthus qu…
## 16 Species -0.800 Violet-tailed Sylph_Heliconia burleana
## 17 Species -0.800 Wedge-billed Hummingbird_Heliconia bur…
## 18 Random -0.700 Collared Inca_Psammisia sodiroi
## 19 Random -0.700 White-whiskered Hermit_Palicourea demi…
Without random model